British Prime Minister Theresa May has tried to reassure millions of Europeans living in Britain that their lives and those of their families will not be disrupted when London leaves the European Union in 2019.

May's post-Brexit residency proposals offer EU nationals "settled status" in Britain with broadly the same rights as native-born English, Scots and Welsh, and the same access to health care, education, welfare and pensions. EU "settlers" would be subject to British law without recourse to the European Court of Justice.

"We want you to stay," May said in a message to the estimated 3.2 million European nationals living in Britain. Her aim, she said, was to "completely reassure" anyone now living legally in Britain that they would not be asked to leave when the country breaks all ties to the EU.

Five years of residence in Britain is required for Europeans who wish to apply to stay on in the country in the future, according to the government proposal. Those already living in Britain but for a shorter period can remain until they are eligible to apply for "settled status." European nationals living permanently in Britain would lose that status, in most cases, if they stay outside the country for more than two years.

May delivered essentially the same proposal last week in Brussels to EU leaders, who said it did not meet all necessary criteria. The European Parliament's chief Brexit negotiator, Guy Verhofstadt, said Monday that "a number of limitations remain worrisome and will have to be carefully assessed."